The Left and media certainly do this, and they do pay a price. It's not as big as the price the Right pays, but they do pay a price. They cry wolf on the identity politics angle, and frankly, they may pay the price by getting a President Trump. And though I didn't vote for Trump and think he's terrible, there's one thing I'll enjoy if he wins - watching the PC Police, disgusting media frauds, and race hustlers crap in their pants for the next four years.
These unprincipled, hypocritical hacks have called every Republican a racist, sexist, homophobe, misogynist, a Nazi, etc. for decades whether they were or weren't. Basically, the truth didn't matter. Now that they're calling Trump those things, tens of millions of voters don't give a crap and tune them out. A good
article on this phenomenon.